Brooklyn1wp
2022-02-28
Answered

If the hypotenuse of a triangle is 12 cm and the measure of its legs are in the ratio $1:2$ , then what are the measures of it’s legs?

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bedevijuo3e

Answered 2022-03-01
Author has **6** answers

Step 1

Here is a way to solve without directly using Pythagoras theorem.

Let a, b and c be the side lengths of the given right triangle such that c is is the length of hypotenuse.

Measure of legs are in the ratio

Let

Let R and r be the circumradius and inradius of right triangle respectively.

We have,

junoon363km

Answered 2022-03-02
Author has **8** answers

Step 1

If the triangle has a hypotenuse, I’ll assume that the triangle is right angled.

Mr. Pythagoras says that the hypotenuse squared = leg 1 squared plus leg 2 squared.

$\text{leg}\text{}1=1x$

$\text{leg}\text{}2=2x$

$\text{leg}\text{}{1}^{2}+\text{leg}\text{}{2}^{2}={\text{hypotenuse}}^{2}$

$\left(1x\right)}^{2}+{\left(2x\right)}^{2}={12}^{2$

$\left(1{x}^{2}\right\})+\left(4{x}^{2}\right)=144$

$5{x}^{2}={12}^{2}$

$x}^{2}=\frac{144}{5$

${x}^{2}=28.8$

$x=5.367\text{}cm$

$2x=2\times 5.367=10.733\text{}cm$

Step 2

Proof:

If both sides of this equation are equal, then the answer is right.

$12}^{2}=\ne {5.367}^{2}+{10.733}^{2$

$144=\ne 28.8+115.2$

$144=144$

One leg of the triangle is 5.367 cm and the second leg is 10.733 cm.

If the triangle has a hypotenuse, I’ll assume that the triangle is right angled.

Mr. Pythagoras says that the hypotenuse squared = leg 1 squared plus leg 2 squared.

Step 2

Proof:

If both sides of this equation are equal, then the answer is right.

One leg of the triangle is 5.367 cm and the second leg is 10.733 cm.

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